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A057474 Numbers n such that x^n + x^5 + 1 is irreducible over GF(2). 1
2, 3, 6, 9, 12, 14, 17, 20, 23, 44, 47, 63, 84, 129, 236, 278, 279, 297, 300, 647, 726, 737, 2574, 2660, 4233, 4500, 8207, 11900, 16046, 21983, 23999, 24596, 24849, 84929, 130926, 156308, 160046, 185142 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Next term is > 10^5. [Joerg Arndt, Apr 28 2012]

Next term is > 241000. - Manfred Scheucher, Aug 18 2015

LINKS

Table of n, a(n) for n=1..38.

Joerg Arndt, Matters Computational (The Fxtbook), section 40.9.3 "Irreducible trinomials of the form 1 + x^k + x^d", p.850

MATHEMATICA

Do[ If[ ToString[ Factor[ x^n + x^5 + 1, Modulus -> 2 ] ] == ToString[ x^n + x^5 + 1 ], Print[ n ] ], {n, 0, 900} ]

PROG

(Sage)

P.<x> = GF(2)[]

for n in range(10^4):

    if (x^n+x^5+1).is_irreducible():

        print(n) # Joerg Arndt, Apr 28 2012

CROSSREFS

Cf. A002475.

Sequence in context: A191981 A131975 A288754 * A270139 A145441 A077121

Adjacent sequences:  A057471 A057472 A057473 * A057475 A057476 A057477

KEYWORD

nonn,hard,more

AUTHOR

Robert G. Wilson v, Sep 27 2000

EXTENSIONS

a(23)-a(34) by Joerg Arndt, Apr 28 2012

a(35)-a(38) by Manfred Scheucher, Aug 18 2015

STATUS

approved

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Last modified February 22 05:17 EST 2019. Contains 320385 sequences. (Running on oeis4.)